The the six-wheeled armoured car Steed arrives in at brigadier Goddard's house is an Alvis Saladin FV601.
The two RAF officers recite a list of countersigns which include "double oh seven," which is James Bond's serial number 007. Later, the hero introduces himself as "Steed, John Steed," similar to "Bond, James Bond." Patrick Macnee, Diana Rigg, John Le Mesurier, and Cecil Paul all appeared in James Bond movies.
The helicopter (G-ASHD) seen (at about 10 minutes in) is a 1963 Brantly B-2A (c/n 314). It was commonly referred to as the "ice cream cone" because of its conical shaped design. It was crashed on 15 February 1967.
To foil eavesdropping microphones, the defence trio zip themselves into a large bag. America's Get Smart (1965), which had been airing for almost a year at this time, had a running gag called the "cone of silence," which served the same strategic and comedic role.